# Electrical Impedance Tomography for Hand Gesture Recognition for HMI Interaction Applications

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State of the Art

## 3. Materials and Method: Experimental Platform

#### 3.1. Measuring System

#### 3.1.1. Type of Measurement

#### 3.1.2. Number of Electrodes and Measurements

#### 3.2. Required Hardware and Software

#### 3.3. Configuration Parameters for Pattern Acquisition

#### 3.4. Pattern Acquisition and Processing

#### 3.5. Pattern Classifier

## 4. Results

#### 4.1. Experimental Results of Data Reading

#### Analysis of the Reading of Experimental Results

- The pattern from 28 measurements to 14 measurements will be called “Reduction A”, abbreviated as RedA;
- The pattern from the first 14 measurements to 7 measurements will be called “Reduction B”, abbreviated as RedB;
- The pattern from the last 14 measurements to 5 measurements will be called “Reduction C”, abbreviated as RedC.

#### 4.2. Experimental Results of Feature Extraction and Selection

#### 4.2.1. Correlation Matrix Results

- H
_{0}states that the set of measurements obtained by each gesture is linearly independent of each other - H
_{1}states that the set of measurements obtained by each gesture is linearly dependent on each other

#### 4.2.2. Experimental Results of Dimensionality Reduction by PCA

#### 4.3. Experimental Results of the Predictive Model

#### Cross-Validation

#### 4.4. Results of the kNN Classification Algorithm and Sensitivity

- Group 1, left gesture and fist;
- Group 2, index-thumb and claw gesture;
- Group 3, thumb gesture and relaxed.

## 5. Discussion

## 6. Conclusions

_{0}and accept the alternative hypothesis H

_{1}. Therefore, the condition is fulfilled so that it is possible to apply principal component analysis to reduce the dimensionality of the dataset. After its application, it was observed that it was possible to work with two main components because they describe, in the worst case, 96% of the data. Bearing in mind that the measurements with the least distance from the lines of each gesture are those located in the first and fourth quadrants, three possible reduced patterns were established; Reduction A from 28 to 14 measurements, Reduction B from 14 to 7 measurements, and Reduction C from 14 to 5 measurements.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Two-wire measurement scheme with eight electrodes: (

**a**) Presents the two-wire measurement system to be used, with A electrode as an emitter and B electrode as a receiver; (

**b**) shows a first loop of measurements with A electrode as an emitter (red arrows represent the measurement pairs) and a second loop of measurements with B electrode as an emitter (blue arrows represent the measurement pairs).

**Figure 2.**Gestures made with the right hand to acquire the impedance patterns. Each gesture is named as: (

**a**) Claw; (

**b**) fist; (

**c**) index-thumb; (

**d**) relaxed; (

**e**) left; and (

**f**) thumb.

**Figure 4.**Impedance patterns from gesture measurements for each combination: (

**a**) Index-thumb gesture; (

**b**) left gesture; (

**c**) fist gesture; (

**d**) claw gesture; (

**e**) thumb gesture; (

**f**) relaxed gesture. Each bioimpedance pattern corresponds to: black, first iteration; red, second iteration; blue, third iteration; pink, fourth iteration; green, fifth iteration.

**Figure 5.**Graph of correlations between each gesture. The linear fit and Pearson’s coefficient are also represented for: (

**a**) Reduction A; (

**b**) Reduction B; (

**c**) Reduction C.

**Figure 6.**Scree graph that relates the eigenvalues with respect to the main components for: (

**a**) Reduction A; (

**b**) Reduction B; (

**c**) Reduction C.

**Figure 7.**Biplot graph that relates Principal Component 2 with respect to Principal Component 1 for: (

**a**) Reduction A; (

**b**) Reduction B; (

**c**) Reduction C.

**Figure 8.**Dimensionality reduction for: (

**a**) Reduction A. Measurements A are indicated in green, measurements B in blue, measurements D in yellow, measurements E in orange, measurements F in black, and measurements G in gray; (

**b**) Reduction B. Measurements A are indicated in green and measurements B in blue; and (

**c**) Reduction C. Measurements E are indicated in orange, measurements F in black, and measurements G in gray.

**Figure 9.**Impedance pattern of each gesture measured for: (

**a**) The 28 measurements; (

**b**) Reduction A; (

**c**) Reduction C. The legend is at follows: black, mean value for index-thumb gesture; red, mean value for left gesture; blue, mean value for fist gesture; pink, mean value for claw gesture; green, mean value for relaxed gesture; dark blue, mean value for thumb gesture.

Parameter | Value |
---|---|

Start frequency | 50 kHz |

Delta frequency | 500 Hz |

Increment number | 100 |

Final frequency | 100 kHz |

Parameter | Value |
---|---|

System clock | External clock |

Output excitation | 1 V_{PP} |

PGA control | Gain = 1 |

Calibration impedance | R1 = 2 kΩ |

**Table 3.**Eigenvalues, variance, and accumulated for each principal component defined for Reduction A. In orange shading, the accumulation greater than 90%.

Component (PCi) | Eigenvalue | Variance (%) | Accumulated |
---|---|---|---|

1 | 5.178 | 86.29% | 86.29% |

2 | 0.413 | 6.89% | 93.18% |

3 | 0.301 | 5.03% | 98.20% |

4 | 0.0681 | 1.14% | 99.34% |

5 | 0.0333 | 0.55% | 99.89% |

6 | 0.00654 | 0.11% | 100.00% |

**Table 4.**Eigenvalues, variance, and accumulated for each principal component defined for Reduction B. In orange shading, the accumulation greater than 90%.

Component (PCi) | Eigenvalue | Variance (%) | Accumulated |
---|---|---|---|

1 | 5.387 | 89.79% | 89.79% |

2 | 0.436 | 7.27% | 97.06% |

3 | 0.145 | 2.43% | 99.49% |

4 | 0.0215 | 0.36% | 99.85% |

5 | 0.00817 | 0.14% | 99.98% |

6 | 9.22 × 10^{−4} | 0.02% | 100.00% |

**Table 5.**Eigenvalues, variance, and accumulated for each principal component defined for Reduction C. In orange shading, the accumulation greater than 90%.

Component (PCi) | Eigenvalue | Variance (%) | Accumulated |
---|---|---|---|

1 | 5.3359 | 88.93% | 88.93% |

2 | 0.447 | 7.46% | 96.39% |

3 | 0.130 | 2.17% | 98.56% |

4 | 0.0773 | 1.29% | 99.85% |

5 | 0.00479 | 0.08% | 99.93% |

6 | 4.02 × 10^{−3} | 0.07% | 100.00% |

**Table 6.**Measurements obtained after applying component analysis for Reduction A, Reduction B, and Reduction C.

Measurements | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

RedA | 4 AE | 5 AF | 6 AG | 10 BE | 11 BF | 12 BG | 13 BH | 21 DG | 23 EF | 24 EG | 25 EH | 26 FG | 27 FH | 28 GH |

RedB | 4 AE | 5 AF | 6 AG | 10 BE | 11 BF | 12 BG | 13 BH | - | - | - | - | - | - | - |

RedC | - | - | - | - | - | - | - | - | - | 24 EG | 25 EH | 26 FG | 27 FH | 28 GH |

**Table 7.**Errors obtained after cross-validation for Reduction A (RedA), Reduction B (RedB), and Reduction C (RedC) for different values of K.

Iteration K | Gesture | Error, RedA | Error, RedB | Error, RedC |
---|---|---|---|---|

K = 2 | Z Index-Thumb (Ω) | 0.930 | 0.432 | 0.874 |

Z Left (Ω) | 0.955 | 0.443 | 0.897 | |

Z Fist (Ω) | 0.953 | 0.442 | 0.895 | |

Z Claw (Ω) | 0.934 | 0.433 | 0.877 | |

Z Relaxed (Ω) | 0.779 | 0.361 | 0.732 | |

Z Thumb (Ω) | 0.958 | 0.444 | 0.900 | |

K = 3 | Z Index-Thumb (Ω) | 0.861 | 0.403 | 0.823 |

Z Left (Ω) | 0.863 | 0.403 | 0.822 | |

Z Fist (Ω) | 0.861 | 0.402 | 0.819 | |

Z Claw (Ω) | 0.858 | 0.399 | 0.813 | |

Z Relaxed (Ω) | 0.836 | 0.389 | 0.790 | |

Z Thumb (Ω) | 0.858 | 0.399 | 0.809 | |

K = 4 | Z Index-Thumb (Ω) | 0.846 | 0.392 | 0.795 |

Z Left (Ω) | 0.868 | 0.403 | 0.815 | |

Z Fist (Ω) | 0.866 | 0.402 | 0.814 | |

Z Claw (Ω) | 0.849 | 0.394 | 0.798 | |

Z Relaxed (Ω) | 0.708 | 0.328 | 0.665 | |

Z Thumb (Ω) | 0.870 | 0.404 | 0.818 | |

K = 5 | Z Index-Thumb (Ω) | 0.872 | 0.405 | 0.819 |

Z Left (Ω) | 0.895 | 0.415 | 0.841 | |

Z Fist (Ω) | 0.893 | 0.414 | 0.839 | |

Z Claw (Ω) | 0.875 | 0.406 | 0.822 | |

Z Relaxed (Ω) | 0.730 | 0.339 | 0.686 | |

Z Thumb (Ω) | 0.897 | 0.416 | 0.843 | |

K = 6 | Z Index-Thumb (Ω) | 0.846 | 0.392 | 0.795 |

Z Left (Ω) | 0.868 | 0.403 | 0.815 | |

Z Fist (Ω) | 0.866 | 0.402 | 0.814 | |

Z Claw (Ω) | 0.849 | 0.394 | 0.798 | |

Z Relaxed (Ω) | 0.708 | 0.328 | 0.665 | |

Z Thumb (Ω) | 0.870 | 0.404 | 0.818 |

**Table 8.**Descriptive parameters mean (x) and standard deviation (δ) for each mean value of the gesture for Reduction A (Red A), Reduction B (Red B), and Reduction C (Red C).

Z Index- Thumb (Ω) | Z Left (Ω) | Z Fist (Ω) | Z Claw (Ω) | Z Relaxed (Ω) | Z Thumb (Ω) | ||
---|---|---|---|---|---|---|---|

Red. A | x | 416.82 | 420.37 | 421.56 | 418.29 | 364.31 | 364.38 |

δ | 13.09 | 20.38 | 24.48 | 14.08 | 12.39 | 10.79 | |

Red. B | x | 414.98 | 415.59 | 412.44 | 416.54 | 363.20 | 362.90 |

δ | 15.24 | 18.93 | 18.31 | 16.79 | 15.01 | 11.39 | |

Red. C | x | 418.67 | 425.15 | 430.68 | 420.05 | 365.41 | 365.86 |

δ | 10.80 | 21.32 | 27.02 | 11.10 | 9.53 | 10.37 |

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**MDPI and ACS Style**

Vaquero-Gallardo, N.; Martínez-García, H.
Electrical Impedance Tomography for Hand Gesture Recognition for HMI Interaction Applications. *J. Low Power Electron. Appl.* **2022**, *12*, 41.
https://doi.org/10.3390/jlpea12030041

**AMA Style**

Vaquero-Gallardo N, Martínez-García H.
Electrical Impedance Tomography for Hand Gesture Recognition for HMI Interaction Applications. *Journal of Low Power Electronics and Applications*. 2022; 12(3):41.
https://doi.org/10.3390/jlpea12030041

**Chicago/Turabian Style**

Vaquero-Gallardo, Noelia, and Herminio Martínez-García.
2022. "Electrical Impedance Tomography for Hand Gesture Recognition for HMI Interaction Applications" *Journal of Low Power Electronics and Applications* 12, no. 3: 41.
https://doi.org/10.3390/jlpea12030041